(1)	$\begin{array}{l}\displaystyle \rho \, u \frac{\partial u}{\partial l} = -\frac{\partial p}{\partial l} + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}\end{array}$

where

$\begin{array}{l}l\end{array}$	distance along the fluid flow streamline
$\begin{array}{l}\theta(l)\end{array}$	inclinational deviation, $\begin{array}{l}\displaystyle \cos \theta = dz/dl\end{array}$
$\begin{array}{l}z(l)\end{array}$	elevation along the 1D flow trajectory
$\begin{array}{l}p\end{array}$	fluid pressure
$\begin{array}{l}\rho\end{array}$	fluid density
$\begin{array}{l}u\end{array}$	superficial velocity of the fluid flow
$\begin{array}{l}g\end{array}$	standard gravity constant
$\begin{array}{l}{\bf f}_{\rm cnt}\end{array}$	volumetric density of all contact forces exerted on fluid body
$\begin{array}{l}{f}_{\rm cnt, l} = {\bf e}_u \cdot {\bf f}_{\rm cnt}\end{array}$	projection of $\begin{array}{l}{\bf f}_{\rm cnt}\end{array}$ onto the unit fluid velocity vector: $\begin{array}{l}{\bf e}_u = { \| {\bf u} \|} ^{-1} \, {\bf u}\end{array}$

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See also